How to make a 2D balance weighting scale?
The simplest way to get the job done is create a three bones armature, setting their heads in every pivot point needed, then parent left and right to main bone (keep offset), then unceck the "inherit rotation" option for both arms.

Then parent every 2D object to the respective bone (Ctrl P - Bone).

After the programming of the animation you can add some noise generator to the f-curves in the graph editor, where you need some random movements.